The acceleration of gravity at the surface of a newly discovered planet is 5.2 m/s^2. An astronaut throws a rock straight up at 10.5 m/s on this planet. How high will it go?
Please help!!!
It will rise until it gains potential energy equal to the initial kinetic energy. That will happen at height H given by
M g H = (M/2) Vo^2
which can be rewritten
H = Vo^2/(2 g)
Use 5.2 m/s^2 for g, not the Earth's surface value of 9.8 m/s^2.
H = 10.6 m
To find out how high the rock will go on the newly discovered planet, we can use the kinematic equations of motion. The first step is to determine the time it takes for the rock to reach its highest point.
We have the initial velocity (vi) of the rock, which is 10.5 m/s, and the acceleration (a) due to gravity on the planet's surface, which is 5.2 m/s^2. Since the rock is thrown straight up, its final velocity (vf) at the highest point will be 0 m/s.
The equation relating initial velocity, final velocity, acceleration, and time is:
vf = vi + at
Substituting the given values:
0 = 10.5 m/s + (5.2 m/s^2) * t
Rearranging the equation, we get:
-10.5 m/s = 5.2 m/s^2 * t
Solving for t:
t = -10.5 m/s / 5.2 m/s^2
t = -2.019 s
Note that the time is negative because we only considered the upward motion. So, it will take approximately 2.019 seconds for the rock to reach its highest point.
Next, to find the maximum height (h), we can use another kinematic equation:
h = vi * t + (1/2) * a * t^2
Substituting the values:
h = 10.5 m/s * 2.019 s + (1/2) * 5.2 m/s^2 * (2.019 s)^2
Calculating:
h = 21.16 m
Therefore, on the newly discovered planet, the rock will reach a maximum height of approximately 21.16 meters.